Provided by: libmath-gsl-perl_0.39-1build2_amd64 
NAME
Math::GSL::Integration - Routines for performing numerical integration (quadrature) of a
function in one dimension
SYNOPSIS
use Math::GSL::Integration qw /:all/;
my $function = sub { $_[0]**2 } ;
my ($lower, $upper ) = (0,1);
my ($relerr,$abserr) = (0,1e-7);
my ($status, $result, $abserr, $num_evals) = gsl_integration_qng ( $function,
$lower, $upper, $relerr, $abserr
);
DESCRIPTION
This module allows you to numerically integrate a Perl subroutine. Depending on the
properties of your function (singularities, smoothness) and the type of integration range
(finite, infinite, semi-infinite), you will need to choose a quadrature routine that fits
your needs.
• "gsl_integration_workspace_alloc($n)"
This function allocates a workspace sufficient to hold $n double precision intervals,
their integration results and error estimates.
• "gsl_integration_workspace_free($w)"
This function frees the memory associated with the workspace $w.
• "gsl_integration_qaws_table_alloc($alpha, $beta, $mu, $nu)"
This function allocates space for a gsl_integration_qaws_table struct
describing a singular weight function W(x) with the parameters ($alpha, $beta,
$mu, $nu), W(x) = (x-a)^alpha (b-x)^beta log^mu (x-a) log^nu (b-x) where
$alpha > -1, $beta > -1, and $mu = 0, 1, $nu = 0, 1. The weight function can
take four different forms depending on the values of $mu and $nu,
W(x) = (x-a)^alpha (b-x)^beta (mu = 0, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) (mu = 1, nu = 0)
W(x) = (x-a)^alpha (b-x)^beta log(b-x) (mu = 0, nu = 1)
W(x) = (x-a)^alpha (b-x)^beta log(x-a) log(b-x) (mu = 1, nu = 1)
The singular points (a,b) do not have to be specified until the integral is computed,
where they are the endpoints of the integration range. The function returns a pointer
to the newly allocated table gsl_integration_qaws_table if no errors were detected,
and 0 in the case of error.
• "gsl_integration_qaws_table_set($t, $alpha, $beta, $mu, $nu)"
This function modifies the parameters ($alpha, $beta, $mu, $nu) of an existing
gsl_integration_qaws_table struct $t.
• "gsl_integration_qaws_table_free($t)"
This function frees all the memory associated with the
gsl_integration_qaws_table struct $t.
• "gsl_integration_qawo_table_alloc($omega, $L, $sine, $n)"
• "gsl_integration_qawo_table_set($t, $omega, $L, $sine, $n)"
This function changes the parameters omega, L and sine of the existing
workspace $t.
• "gsl_integration_qawo_table_set_length($t, $L)"
This function allows the length parameter $L of the workspace $t to be
changed.
• "gsl_integration_qawo_table_free($t)"
This function frees all the memory associated with the workspace $t.
• "gsl_integration_qk15($function,$a,$b,$resabs,$resasc) "
• "gsl_integration_qk21($function,$a,$b,$resabs,$resasc) "
• "gsl_integration_qk31($function,$a,$b,$resabs,$resasc) "
• "gsl_integration_qk41($function,$a,$b,$resabs,$resasc) "
• "gsl_integration_qk51($function,$a,$b,$resabs,$resasc) "
• "gsl_integration_qk61($function,$a,$b,$resabs,$resasc) "
• "gsl_integration_qcheb($function, $a, $b, $cheb12, $cheb24) "
• "gsl_integration_qk "
• "gsl_integration_qng($function,$a,$b,$epsabs,$epsrel,$num_evals) "
This routine QNG (Quadrature Non-Adaptive Gaussian) is inexpensive is the sense that
it will evaluate the function much fewer times than the adaptive routines. Because of
this it does not need any workspaces, so it is also more memory efficient. It should
be perfectly fine for well-behaved functions (smooth and nonsingular), but will not be
able to get the required accuracy or may not converge for more complicated functions.
• "gsl_integration_qag($function,$a,$b,$epsabs,$epsrel,$limit,$key,$workspace) "
This routine QAG (Quadrature Adaptive Gaussian) ...
• "gsl_integration_qagi($function,$epsabs,$epsrel,$limit,$workspace) "
• "gsl_integration_qagiu($function,$a,$epsabs,$epsrel,$limit,$workspace) "
• "gsl_integration_qagil($function,$b,$epsabs,$epsrel,$limit,$workspace) "
• "gsl_integration_qags($func,$a,$b,$epsabs,$epsrel,$limit,$workspace)"
($status, $result, $abserr) = gsl_integration_qags (
sub { 1/$_[0]} ,
1, 10, 0, 1e-7, 1000,
$workspace,
);
This function applies the Gauss-Kronrod 21-point integration rule
adaptively until an estimate of the integral of $func over ($a,$b) is
achieved within the desired absolute and relative error limits,
$epsabs and $epsrel.
• "gsl_integration_qagp($function, $pts, $npts, $epsbs, $epsrel, $limit, $workspace) "
• "gsl_integration_qawc($function, $a, $b, $c, $epsabs, $epsrel, $limit, $workspace) "
• "gsl_integration_qaws($function, $a, $b, $qaws_table, $epsabs, $epsrel, $limit,
$workspace) "
• "gsl_integration_qawo($function, $a, $epsabs, $epsrel, $limit, $workspace,
$qawo_table) "
• "gsl_integration_qawf($function, $a, $epsabs, $limit, $workspace, $cycle_workspace,
$qawo_table) "
This module also includes the following constants :
• $GSL_INTEG_COSINE
• $GSL_INTEG_SINE
• $GSL_INTEG_GAUSS15
• $GSL_INTEG_GAUSS21
• $GSL_INTEG_GAUSS31
• $GSL_INTEG_GAUSS41
• $GSL_INTEG_GAUSS51
• $GSL_INTEG_GAUSS61
The following error constants are part of the Math::GSL::Errno module and can be returned
by the gsl_integration_* functions :
• $GSL_EMAXITER
Maximum number of subdivisions was exceeded.
• $GSL_EROUND
Cannot reach tolerance because of roundoff error, or roundoff error was detected in
the extrapolation table.
• GSL_ESING
A non-integrable singularity or other bad integrand behavior was found in the
integration interval.
• GSL_EDIVERGE
The integral is divergent, or too slowly convergent to be integrated numerically.
MORE INFO
For more information on the functions, we refer you to the GSL offcial documentation:
<http://www.gnu.org/software/gsl/manual/html_node/>
AUTHORS
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
COPYRIGHT AND LICENSE
Copyright (C) 2008-2011 Jonathan "Duke" Leto and Thierry Moisan
This program is free software; you can redistribute it and/or modify it under the same
terms as Perl itself.